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Journal articles on the topic 'Hawke Process'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

van Hattum, Jop, and Victoria Jackson. "Structural reform and petroleum (environment) regulations in the Northern Territory." APPEA Journal 56, no. 2 (2016): 565. http://dx.doi.org/10.1071/aj15071.

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The opportunity for onshore oil and gas development in the Northern Territory (NT) has grown exponentially in recent years, driven by the NT’s expansive shale gas resources in the McArthur Basin and elsewhere. Such resources provide many potential benefits to the territory’s economy, including job creation and clean, cost-effective energy generation opportunities. Critical to the successful development of the industry is a legitimate social licence to operate with the community, for which strong environmental regulation is a key enabling factor. Communities must be assured that oil and gas activities can provide ecologically sustainable development, and a transparent, evidence- and risk-based framework is the best way to achieve this. Following the NT Inquiry into Hydraulic Fracturing by Dr Allan Hawke in November 2014, and further review of the environmental assessment and approval processes in May 2015, the NT Government has implemented structural reform and developed contemporary outcome-focused Petroleum (Environment) Regulations to balance environmental protection with the economic development benefits offered by the onshore gas industry. Those objectives include that petroleum development in the NT: is consistent with the principles of ecologically sustainable development; reduces risks and impacts to levels that are as low as reasonably practicable and acceptable; ensures meaningful engagement with stakeholder; and, provides for transparency of decision-making and publication of approved environment management plans in full. This extended abstract provides an update of the reform of the regulatory framework, the regulatory objectives, the regulations by which they’re achieved, and the consultation process followed to gain wide stakeholder support. It will also highlight that strong regulations alone do not provide a robust regulatory framework, and the steps the NT Government is taking to achieve its objective. The regulations are planned to come into force in the third quarter of 2016. Meanwhile, a full review of the NT Petroleum Act and development of Petroleum (Resource Management) Regulations that takes into consideration the recommendations from the Hawke Inquiry into Hydraulic Fracturing in the NT is underway.

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2

Doğan, Emrah, and Cenk Elibol. "The Comparative Analysis of Landsberg and Friedman and Stammberger and Hawke Computer Tomography Classifications in the Superior Attachment of the Nasal Uncinate Process (SAUP) and Potential Pitfalls in Evaluation." Timisoara Medical Journal 2022, no. 2 (September 30, 2022): 1. http://dx.doi.org/10.35995/tmj20220205.

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(1) Object: Our study aims to identify the common and diverging points in the superior attachment of the nasal uncinate process (SAUP) classifications and to draw attention to the pitfalls in these evaluation processes. (2) Material and Methods: This study was performed on 200 patients (males/females, 100/100; mean age/range: 37.13 ± 16.14/16–84), and 400 sides were bilaterally evaluated. Potential pitfalls were investigated. All UPs were classified according to the Landsberg and Friedman (LF) and Stammberger and Hawke (SH) classifications, and these two classifications were compared. (3) Results: There was a high statistically significant correlation between SH and LF. SH Type IV and LF Type 0 and SH Type III and LF Type 6 completely overlapped. SH Type I corresponded to LF Types 2 and 3 and SH Type II to LF Type 2, 3, 4, and 5 groups. There was no significant difference between genders or sides (right and left) in terms of the LF or SH classifications. (4): Conclusions: Following the thick band and paying attention to concavity and convexity helps to accurately evaluate the anatomical structure. Only two groups overlapped one to one. For SH Types II and III, and LF Types 1, 2, 3, 4, and 5, knowing the SAUP group in one classification does not give an exact idea about the group of the other classification. Therefore, it is not possible to make comparisons between reports or studies using different classifications.

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3

Moreno Trujillo, John Freddy. "Modelo estocástico para el precio de activos riesgosos utilizando procesos Hawkes." ODEON, no. 15 (May 13, 2019): 161–72. http://dx.doi.org/10.18601/17941113.n15.06.

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El documento presenta los elementos básicos para entender los procesos Hawkes y su aplicación en finanzas. Se caracteriza el comportamiento asintótico de estos procesos y se describe el proceso de difusión de Hawkes como modelo para el retorno logarítmico de activos riesgosos en continuo.

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4

Badcock, B. A., and M. A. Browett. "Adelaide's Heart Transplant, 1970–88: 3. The Deployment of Capital in the Renovation and Redevelopment Submarkets." Environment and Planning A: Economy and Space 24, no. 8 (August 1992): 1167–90. http://dx.doi.org/10.1068/a241167.

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In this, the last of three papers devoted to urban restructuring and its impact upon the built environment of an Australian city, the spatial focus narrows from the metropolitan region to an inner zone of Adelaide. This is the part of Adelaide that has gained most from the processes of residential reinvestment and gentrification over the last two decades. The interest in the circulation of capital that has been maintained throughout the previous papers is explored more fully by measuring and evaluating investment activity in the renovation and redevelopment submarkets. The evidence presented on the organizational structure, levels of investment, and returns to investment within the two submarkets makes for a better-informed characterization of ‘property capital’. It also serves to make the accompanying role of public finance in the revitalization process much clearer. In this paper, the interpretation of capital formation in the renovation and redevelopment submarkets suggests that all three tiers of government in Australia have been thoroughly implicated in the residential transformation of Inner Adelaide during the last two decades. Changes to the Commonwealth States Housing Agreement in 1973 released public funds for rehabilitating terrace housing in the City and inner suburbs, and the Hawke Government restructured taxation policy and the financial markets affecting investment in the home unit and town house submarket in the 1980s. Meanwhile the Dunstan administration in South Australia axed the freeway and high-rise-housing plans of the previous state government, and pressured City Hall to abandon its grandiose plans for commercializing the City's ‘square mile’. The residential development policies conceived in the mid-1970s as part of the replacement City of Adelaide Plan were emulated by other local government bodies in the nearby suburbs. Somewhat uncharacteristically, the state's public-housing agency gave a lead to project developers in the private sector by demonstrating what could be achieved in the submarket of inner-city-home units and town houses.

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5

Rhee, Byung-Kun. "A Study on the Jump Transmission among Asian Stock Markets Using Hawkes Process." Journal of Economic Studies 36, no. 2 (May 31, 2018): 179–203. http://dx.doi.org/10.30776/jes.36.2.8.

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6

Malem-Shinitski, Noa, César Ojeda, and Manfred Opper. "Variational Bayesian Inference for Nonlinear Hawkes Process with Gaussian Process Self-Effects." Entropy 24, no. 3 (February 28, 2022): 356. http://dx.doi.org/10.3390/e24030356.

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Traditionally, Hawkes processes are used to model time-continuous point processes with history dependence. Here, we propose an extended model where the self-effects are of both excitatory and inhibitory types and follow a Gaussian Process. Whereas previous work either relies on a less flexible parameterization of the model, or requires a large amount of data, our formulation allows for both a flexible model and learning when data are scarce. We continue the line of work of Bayesian inference for Hawkes processes, and derive an inference algorithm by performing inference on an aggregated sum of Gaussian Processes. Approximate Bayesian inference is achieved via data augmentation, and we describe a mean-field variational inference approach to learn the model parameters. To demonstrate the flexibility of the model we apply our methodology on data from different domains and compare it to previously reported results.

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7

Seol, Youngsoo. "Non-Markovian Inverse Hawkes Processes." Mathematics 10, no. 9 (April 22, 2022): 1413. http://dx.doi.org/10.3390/math10091413.

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Hawkes processes are a class of self-exciting point processes with a clustering effect whose jump rate is determined by its past history. They are generally regarded as continuous-time processes and have been widely applied in a number of fields, such as insurance, finance, queueing, and statistics. The Hawkes model is generally non-Markovian because its future development depends on the timing of past events. However, it can be Markovian under certain circumstances. If the exciting function is an exponential function or a sum of exponential functions, the model can be Markovian with a generator of the model. In contrast to the general Hawkes processes, the inverse Hawkes process has some specific features and self-excitation indicates severity. Inverse Markovian Hawkes processes were introduced by Seol, who studied some asymptotic behaviors. An extended version of inverse Markovian Hawkes processes was also studied by Seol. With this paper, we propose a non-Markovian inverse Hawkes process, which is a more general inverse Hawkes process that features several existing models of self-exciting processes. In particular, we established both the law of large numbers (LLN) and Central limit theorems (CLT) for a newly considered non-Markovian inverse Hawkes process.

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8

Liyi Zhang, Liyi Zhang, Zuochen Ren Liyi Zhang, Ting Liu Zuochen Ren, and Jinyan Tang Ting Liu. "Improved Artificial Bee Colony Algorithm Based on Harris Hawks Optimization." 網際網路技術學刊 23, no. 2 (March 2022): 379–89. http://dx.doi.org/10.53106/160792642022032302016.

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<p>Artificial bee colony algorithm, as a kind of bio-like intelligent algorithm, used by various optimization problems because of its few parameters and simple structure. However, there are also shortcomings such as low convergence accuracy, slow convergence speed, and not easy to jump out of the local optimum. Aiming at this shortcoming, this paper proposes an evolutionary algorithm of improved artificial bee colony algorithm based on reverse learning Harris Hawk (HABC). The basic inspiration of HABC comes from the good convergence of Harris Hawk algorithm in the process of finding the best point of the function. First, introduce the Harris Hawks optimization progressive rapid dives stage in the onlooker bee phase to speed up the algorithm convergence; Secondly, Cauchy reverse learning is added in the scout phase to make the algorithm development more promising areas in order to find a better solution; Finally, 13 standard test functions and CEC-C06 2019 benchmark test results are used to test the proposed HABC algorithm and compare with ABC, Markov Chain based artificial bee colony algorithm (MABC), dragonfly algorithm (DA), particle swarm optimization (PSO), learner performance based behavior algorithm (LPB), and fitness dependent optimizer (FDO). Compared with other algorithms, the convergence speed, optimization accuracy and algorithm success rate of the HABC algorithm are relatively excellent.</p> <p> </p>

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9

Zhang, Lu-ning, Jian-wei Liu, Zhi-yan Song, and Xin Zuo. "Temporal attention augmented transformer Hawkes process." Neural Computing and Applications 34, no. 5 (November 8, 2021): 3795–809. http://dx.doi.org/10.1007/s00521-021-06641-z.

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10

Jang, Hyun Jin, Han-Gyun Woo, and Changyong Lee. "Hawkes process-based technology impact analysis." Journal of Informetrics 11, no. 2 (May 2017): 511–29. http://dx.doi.org/10.1016/j.joi.2017.03.007.

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11

Zhu, Lingjiong. "Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps." Journal of Applied Probability 51, no. 3 (September 2014): 699–712. http://dx.doi.org/10.1239/jap/1409932668.

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In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. We obtain Laplace transforms and limit theorems, including the law of large numbers, central limit theorems, and large deviations.

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12

Zhu, Lingjiong. "Limit Theorems for a Cox-Ingersoll-Ross Process with Hawkes Jumps." Journal of Applied Probability 51, no. 03 (September 2014): 699–712. http://dx.doi.org/10.1017/s002190020001161x.

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In this paper we propose a stochastic process, which is a Cox-Ingersoll-Ross process with Hawkes jumps. It can be seen as a generalization of the classical Cox-Ingersoll-Ross process and the classical Hawkes process with exponential exciting function. Our model is a special case of the affine point processes. We obtain Laplace transforms and limit theorems, including the law of large numbers, central limit theorems, and large deviations.

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13

Zhang, Rui, Christian Walder, and Marian-Andrei Rizoiu. "Variational Inference for Sparse Gaussian Process Modulated Hawkes Process." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6803–10. http://dx.doi.org/10.1609/aaai.v34i04.6160.

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The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the non-parametric Bayesian HP has been proposed. However, the inference of such models suffers from unscalability or slow convergence. In this paper, we aim to solve both problems. Specifically, first, we propose a new non-parametric Bayesian HP in which the triggering kernel is modeled as a squared sparse Gaussian process. Then, we propose a novel variational inference schema for model optimization. We employ the branching structure of the HP so that maximization of evidence lower bound (ELBO) is tractable by the expectation-maximization algorithm. We propose a tighter ELBO which improves the fitting performance. Further, we accelerate the novel variational inference schema to linear time complexity by leveraging the stationarity of the triggering kernel. Different from prior acceleration methods, ours enjoys higher efficiency. Finally, we exploit synthetic data and two large social media datasets to evaluate our method. We show that our approach outperforms state-of-the-art non-parametric frequentist and Bayesian methods. We validate the efficiency of our accelerated variational inference schema and practical utility of our tighter ELBO for model selection. We observe that the tighter ELBO exceeds the common one in model selection.

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14

Brémaud, P., G. Nappo, and G. L. Torrisi. "Rate of convergence to equilibrium of marked Hawkes processes." Journal of Applied Probability 39, no. 1 (March 2002): 123–36. http://dx.doi.org/10.1239/jap/1019737993.

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In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

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15

Brémaud, P., G. Nappo, and G. L. Torrisi. "Rate of convergence to equilibrium of marked Hawkes processes." Journal of Applied Probability 39, no. 01 (March 2002): 123–36. http://dx.doi.org/10.1017/s0021900200021562.

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In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

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16

Koops, D. T., M. Saxena, O. J. Boxma, and M. Mandjes. "Infinite-server queues with Hawkes input." Journal of Applied Probability 55, no. 3 (September 2018): 920–43. http://dx.doi.org/10.1017/jpr.2018.58.

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Abstract In this paper we study the number of customers in infinite-server queues with a self-exciting (Hawkes) arrival process. Initially we assume that service requirements are exponentially distributed and that the Hawkes arrival process is of a Markovian nature. We obtain a system of differential equations that characterizes the joint distribution of the arrival intensity and the number of customers. Moreover, we provide a recursive procedure that explicitly identifies (transient and stationary) moments. Subsequently, we allow for non-Markovian Hawkes arrival processes and nonexponential service times. By viewing the Hawkes process as a branching process, we find that the probability generating function of the number of customers in the system can be expressed in terms of the solution of a fixed-point equation. We also include various asymptotic results: we derive the tail of the distribution of the number of customers for the case that the intensity jumps of the Hawkes process are heavy tailed, and we consider a heavy-traffic regime. We conclude by discussing how our results can be used computationally and by verifying the numerical results via simulations.

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17

Ilyas, N., N. Sunusi, Anisa, and St Sahriman. "Likelihood Construction of Hawkes Process in Insurance Claim Settlement Process." Journal of Physics: Conference Series 1341 (October 2019): 092016. http://dx.doi.org/10.1088/1742-6596/1341/9/092016.

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18

Seol, Youngsoo. "Limit theorems for inverse process T n of Hawkes process." Acta Mathematica Sinica, English Series 33, no. 1 (September 29, 2016): 51–60. http://dx.doi.org/10.1007/s10114-016-5470-y.

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19

Fierro, Raúl, Víctor Leiva, and Jesper Møller. "The Hawkes Process with Different Exciting Functions and its Asymptotic Behavior." Journal of Applied Probability 52, no. 1 (March 2015): 37–54. http://dx.doi.org/10.1239/jap/1429282605.

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The standard Hawkes process is constructed from a homogeneous Poisson process and uses the same exciting function for different generations of offspring. We propose an extension of this process by considering different exciting functions. This consideration may be important in a number of fields; e.g. in seismology, where main shocks produce aftershocks with possibly different intensities. The main results are devoted to the asymptotic behavior of this extension of the Hawkes process. Indeed, a law of large numbers and a central limit theorem are stated. These results allow us to analyze the asymptotic behavior of the process when unpredictable marks are considered.

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20

Fierro, Raúl, Víctor Leiva, and Jesper Møller. "The Hawkes Process with Different Exciting Functions and its Asymptotic Behavior." Journal of Applied Probability 52, no. 01 (March 2015): 37–54. http://dx.doi.org/10.1017/s0021900200012183.

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The standard Hawkes process is constructed from a homogeneous Poisson process and uses the same exciting function for different generations of offspring. We propose an extension of this process by considering different exciting functions. This consideration may be important in a number of fields; e.g. in seismology, where main shocks produce aftershocks with possibly different intensities. The main results are devoted to the asymptotic behavior of this extension of the Hawkes process. Indeed, a law of large numbers and a central limit theorem are stated. These results allow us to analyze the asymptotic behavior of the process when unpredictable marks are considered.

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21

Kirchner, Matthias. "An estimation procedure for the Hawkes process." Quantitative Finance 17, no. 4 (September 12, 2016): 571–95. http://dx.doi.org/10.1080/14697688.2016.1211312.

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22

Wang, Ting, Mark Bebbington, and David Harte. "Markov-modulated Hawkes process with stepwise decay." Annals of the Institute of Statistical Mathematics 64, no. 3 (December 30, 2010): 521–44. http://dx.doi.org/10.1007/s10463-010-0320-7.

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23

Swishchuk, Anatoliy. "Risk Model Based on Compound Hawkes Process." Wilmott 2018, no. 94 (March 2018): 50–57. http://dx.doi.org/10.1002/wilm.10662.

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24

Morariu-Patrichi, Maxime, and Mikko S. Pakkanen. "Hybrid Marked Point Processes: Characterization, Existence and Uniqueness." Market Microstructure and Liquidity 04, no. 03n04 (September 2018): 1950007. http://dx.doi.org/10.1142/s2382626619500072.

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In this paper, we introduce a class of hybrid marked point processes, which encompasses and extends continuous-time Markov chains and Hawkes processes. While this flexible class amalgamates such existing processes, it also contains novel processes with complex dynamics. These processes are defined implicitly via their intensity and are endowed with a state process that interacts with past-dependent events. The key example we entertain is an extension of a Hawkes process, a state-dependent Hawkes process interacting with its state process. We show the existence and uniqueness of hybrid marked point processes under general assumptions, extending the results of Massoulié (1998) on interacting point processes.

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25

Brémaud, Pierre, and Laurent Massoulié. "Hawkes branching point processes without ancestors." Journal of Applied Probability 38, no. 1 (March 2001): 122–35. http://dx.doi.org/10.1239/jap/996986648.

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In this article, we prove the existence of critical Hawkes point processes with a finite average intensity, under a heavy-tail condition for the fertility rate which is related to a long-range dependence property. Criticality means that the fertility rate integrates to 1, and corresponds to the usual critical branching process, and, in the context of Hawkes point processes with a finite average intensity, it is equivalent to the absence of ancestors. We also prove an ergodic decomposition result for stationary critical Hawkes point processes as a mixture of critical Hawkes point processes, and we give conditions for weak convergence to stationarity of critical Hawkes point processes.

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Brémaud, Pierre, and Laurent Massoulié. "Hawkes branching point processes without ancestors." Journal of Applied Probability 38, no. 01 (March 2001): 122–35. http://dx.doi.org/10.1017/s0021900200018556.

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In this article, we prove the existence of critical Hawkes point processes with a finite average intensity, under a heavy-tail condition for the fertility rate which is related to a long-range dependence property. Criticality means that the fertility rate integrates to 1, and corresponds to the usual critical branching process, and, in the context of Hawkes point processes with a finite average intensity, it is equivalent to the absence of ancestors. We also prove an ergodic decomposition result for stationary critical Hawkes point processes as a mixture of critical Hawkes point processes, and we give conditions for weak convergence to stationarity of critical Hawkes point processes.

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Yu, Liu, Xovee Xu, Ting Zhong, Goce Trajcevski, and Fan Zhou. "Linking Transformer to Hawkes Process for Information Cascade Prediction (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 11 (June 28, 2022): 13103–4. http://dx.doi.org/10.1609/aaai.v36i11.21688.

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Information cascade is typically formalized as a process of (simplified) discrete sequence of events, and recent approaches have tackled its prediction via variants of recurrent neural networks. However, the information diffusion process is essentially an evolving directed acyclic graph (DAG) in the continuous-time domain. In this paper, we propose a transformer enhanced Hawkes process (Hawkesformer), which links the hierarchical attention mechanism with Hawkes process to model the arrival stream of discrete events continuously. A two-level attention architecture is used to parameterize the intensity function of Hawkesformer, which captures the long-term dependencies between nodes in graph and better embeds the cascade evolution rate for modeling short-term outbreaks. Experimental results demonstrate the significant improvements of Hawkesformer over the state-of-the-art.

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28

Zhang, Bin, Hongyi Lu, Shun Liu, Yucheng Yang, and Doudou Sang. "Aero-Engine Rotor Assembly Process Optimization Based on Improved Harris Hawk Algorithm." Aerospace 10, no. 1 (December 28, 2022): 28. http://dx.doi.org/10.3390/aerospace10010028.

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Multi-stage disc rotor assembly is an important part of the aero-engine rotor manufacturing process. To solve the problem that excessive unbalance of assembly affects the vibration of the whole machine, this paper presents an optimization method for aero-engine rotor assembly balance based on an improved Harris Hawk algorithm. Firstly, the assembly sequence model of the single-stage disc blade and the phase assembly model of a multi-stage disc of the engine rotor is established. Secondly, by using the initial population generation based on dynamic opposing learning and the escape energy function of the non-linear logarithmic convergence factor, the search mechanism of the whale optimization algorithm is introduced in the global exploration, and the adaptive weight strategy and mutation strategy of the genetic algorithm is introduced in the development to improve the algorithm. Then, the effectiveness of the algorithm is verified by experiments and compared with particle swarm optimization, genetic algorithm, and Harris Hawk algorithm, the unbalance of the optimal blade assembly sequence is reduced by 91.75%, 99.82%, and 83.39%, respectively. The algorithm comparison and analysis are carried out for all disc-blade assembly optimization of the rotor. The optimal unbalance of the improved Harris Hawk optimization algorithm is reduced by 79.71%, 99.48%, and 54.92% on average. The unbalance of the algorithm in this paper is the best. Finally, the improved Harris Hawk algorithm is used to find the best assembly phase, and the optimized unbalanced force and moment are reduced by 84.22% and 98.05%, respectively. The results of this study prove that the improved Harris Hawk algorithm for aero-engine rotor assembly balance optimization can effectively reduce the unbalance of rotor disc blade assembly and rotor unbalance and provide a powerful solution for solving engine vibration.

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Bernis, Guillaume, Riccardo Brignone, Simone Scotti, and Carlo Sgarra. "A Gamma Ornstein–Uhlenbeck model driven by a Hawkes process." Mathematics and Financial Economics 15, no. 4 (March 24, 2021): 747–73. http://dx.doi.org/10.1007/s11579-021-00295-0.

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AbstractWe propose an extension of the $$\Gamma $$ Γ -OU Barndorff-Nielsen and Shephard model taking into account jump clustering phenomena. We assume that the intensity process of the Hawkes driver coincides, up to a constant, with the variance process. By applying the theory of continuous-state branching processes with immigration, we prove existence and uniqueness of strong solutions of the SDE governing the asset price dynamics. We propose a measure change of self-exciting Esscher type in order to describe the relation between the risk-neutral and the historical dynamics, showing that the $$\Gamma $$ Γ -OU Hawkes framework is stable under this probability change. By exploiting the affine features of the model we provide an explicit form for the Laplace transform of the asset log-return, for its quadratic variation and for the ergodic distribution of the variance process. We show that the proposed model exhibits a larger flexibility in comparison with the $$\Gamma $$ Γ -OU model, in spite of the same number of parameters required. We calibrate the model on market vanilla option prices via characteristic function inversion techniques, we study the price sensitivities and propose an exact simulation scheme. The main financial achievement is that implied volatility of options written on VIX is upward shaped due to the self-exciting property of Hawkes processes, in contrast with the usual downward slope exhibited by the $$\Gamma $$ Γ -OU Barndorff-Nielsen and Shephard model.

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30

Zhu, Lingjiong. "Central Limit Theorem for Nonlinear Hawkes Processes." Journal of Applied Probability 50, no. 3 (September 2013): 760–71. http://dx.doi.org/10.1239/jap/1378401234.

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The Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central limit theorem for the nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.

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Zhu, Lingjiong. "Central Limit Theorem for Nonlinear Hawkes Processes." Journal of Applied Probability 50, no. 03 (September 2013): 760–71. http://dx.doi.org/10.1017/s0021900200009827.

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The Hawkes process is a self-exciting point process with clustering effect whose intensity depends on its entire past history. It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central limit theorem for the nonlinear Hawkes process. Under the same assumptions, we also obtain a Strassen's invariance principle, i.e. a functional law of the iterated logarithm.

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32

Embrechts, Paul, Thomas Liniger, and Lu Lin. "Multivariate Hawkes processes: an application to financial data." Journal of Applied Probability 48, A (August 2011): 367–78. http://dx.doi.org/10.1239/jap/1318940477.

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A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

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Embrechts, Paul, Thomas Liniger, and Lu Lin. "Multivariate Hawkes processes: an application to financial data." Journal of Applied Probability 48, A (August 2011): 367–78. http://dx.doi.org/10.1017/s0021900200099344.

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A Hawkes process is also known under the name of a self-exciting point process and has numerous applications throughout science and engineering. We derive the statistical estimation (maximum likelihood estimation) and goodness-of-fit (mainly graphical) for multivariate Hawkes processes with possibly dependent marks. As an application, we analyze two data sets from finance.

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34

Brémaud, P., and L. Massoulié. "Power spectra of general shot noises and Hawkes point processes with a random excitation." Advances in Applied Probability 34, no. 1 (March 2002): 205–22. http://dx.doi.org/10.1239/aap/1019160957.

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We give (i) the Cramér power spectral measure of the general shot noise process with random excitation and non-Poisson stationary driving point processes and (ii) the Bartlett power spectral measure of the self-exciting Hawkes point process with random excitation, also called the Hawkes branching point process with random fertility rate. The latter is obtained via the isometry formula for integrals with respect to the canonical martingale measure associated with a marked point process.

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Brémaud, P., and L. Massoulié. "Power spectra of general shot noises and Hawkes point processes with a random excitation." Advances in Applied Probability 34, no. 01 (March 2002): 205–22. http://dx.doi.org/10.1017/s0001867800011460.

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We give (i) the Cramér power spectral measure of the general shot noise process with random excitation and non-Poisson stationary driving point processes and (ii) the Bartlett power spectral measure of the self-exciting Hawkes point process with random excitation, also called the Hawkes branching point process with random fertility rate. The latter is obtained via the isometry formula for integrals with respect to the canonical martingale measure associated with a marked point process.

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Kim, Jooseong. "“The Hawk” and Yeats’s Decolonization Process*1)." Yeats Journal of Korea 27 (June 30, 2007): 155–71. http://dx.doi.org/10.14354/yjk.2007.27.155.

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Legros, Benjamin. "Transient analysis of an affine Queue-Hawkes process." Operations Research Letters 49, no. 3 (May 2021): 393–99. http://dx.doi.org/10.1016/j.orl.2021.04.001.

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Zhang, Lu-ning, Jian-wei Liu, Zhi-yan Song, and Xin Zuo. "Universal transformer Hawkes process with adaptive recursive iteration." Engineering Applications of Artificial Intelligence 105 (October 2021): 104416. http://dx.doi.org/10.1016/j.engappai.2021.104416.

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Le, Triet M. "A Multivariate Hawkes Process With Gaps in Observations." IEEE Transactions on Information Theory 64, no. 3 (March 2018): 1800–1811. http://dx.doi.org/10.1109/tit.2017.2735963.

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Chen, Feng, and Tom Stindl. "Direct Likelihood Evaluation for the Renewal Hawkes Process." Journal of Computational and Graphical Statistics 27, no. 1 (January 2, 2018): 119–31. http://dx.doi.org/10.1080/10618600.2017.1341324.

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Seol, Youngsoo. "Limit theorems for an inverse Markovian Hawkes process." Statistics & Probability Letters 155 (December 2019): 108580. http://dx.doi.org/10.1016/j.spl.2019.108580.

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Hainaut, Donatien. "A bivariate Hawkes process for interest rate modeling." Economic Modelling 57 (September 2016): 180–96. http://dx.doi.org/10.1016/j.econmod.2016.04.016.

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Watari, Hiroki, Hideki Takayasu, and Misako Takayasu. "Analysis of Individual High-Frequency Traders’ Buy–Sell Order Strategy Based on Multivariate Hawkes Process." Entropy 24, no. 2 (January 29, 2022): 214. http://dx.doi.org/10.3390/e24020214.

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Traders who instantly react to changes in the financial market and place orders in milliseconds are called high-frequency traders (HFTs). HFTs have recently become more prevalent and attracting attention in the study of market microstructures. In this study, we used data to track the order history of individual HFTs in the USD/JPY forex market to reveal how individual HFTs interact with the order book and what strategies they use to place their limit orders. Specifically, we introduced an 8-dimensional multivariate Hawkes process that included the excitations due to the occurrence of limit orders, cancel orders, and executions in the order book change, and performed maximum likelihood estimations of the limit order processes for 134 HFTs. As a result, we found that the limit order generation processes of 104 of the 134 HFTs were modeled by a multivariate Hawkes process. In this analysis of the EBS market, the HFTs whose strategies were modeled by the Hawkes process were categorized into three groups according to their excitation mechanisms: (1) those excited by executions; (2) those that were excited by the occurrences or cancellations of limit orders; and (3) those that were excited by their own orders.

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Yu, Chao, Jianxin Bi, and Xujie Zhao. "Modeling Financial Intraday Jump Tail Contagion with High Frequency Data Using Mutually Exciting Hawkes Process." Discrete Dynamics in Nature and Society 2020 (May 20, 2020): 1–10. http://dx.doi.org/10.1155/2020/7940647.

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Financial extreme jumps in asset price may propagate across stock markets and lead to the market-wide crashes, which severely threatens the stability of the financial system. In order to analyzing the contagion features of jump tail risk, this paper proposes a mutually exciting contagion model based on Hawkes process with intraday high frequency data. We use a simple two-stage method that first extracts the jump component nonparametrically from the high frequency data and then models the intraday jump tail using mutually exciting Hawkes process. Moreover, we take both the occurrence time and magnitude of jump into account in modeling the conditional intensity of Hawkes process. The proposed method is applied to the five-minute high frequency data of the Chinese stock market. The empirical results show that, for the two main Chinese stock markets, only background intensity is significant in the Shanghai stock market, while mutually exciting effect is significant in the Shenzhen stock market. Both the location and size of jump in the Shanghai stock market have significant stimulation to the next occurrences of jump in the Shenzhen stock market. Furthermore, the proposed model performs very well in predicting the future jump tail events.

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Shang, Jin, and Mingxuan Sun. "Geometric Hawkes Processes with Graph Convolutional Recurrent Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 4878–85. http://dx.doi.org/10.1609/aaai.v33i01.33014878.

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Hawkes processes are popular for modeling correlated temporal sequences that exhibit mutual-excitation properties. Existing approaches such as feature-enriched processes or variations of Multivariate Hawkes processes either fail to describe the exact mutual influence between sequences or become computational inhibitive in most real-world applications involving large dimensions. Incorporating additional geometric structure in the form of graphs into Hawkes processes is an effective and efficient way for improving model prediction accuracy. In this paper, we propose the Geometric Hawkes Process (GHP) model to better correlate individual processes, by integrating Hawkes processes and a graph convolutional recurrent neural network. The deep network structure is computational efficient since it requires constant parameters that are independent of the graph size. The experiment results on real-world data show that our framework outperforms recent state-of-art methods.

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Swishchuk, Anatoliy. "Merton Investment Problems in Finance and Insurance for the Hawkes-Based Models." Risks 9, no. 6 (June 3, 2021): 108. http://dx.doi.org/10.3390/risks9060108.

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We show how to solve Merton optimal investment stochastic control problem for Hawkes-based models in finance and insurance (Propositions 1 and 2), i.e., for a wealth portfolio X(t) consisting of a bond and a stock price described by general compound Hawkes process (GCHP), and for a capital R(t) (risk process) of an insurance company with the amount of claims described by the risk model based on GCHP. The main approach in both cases is to use functional central limit theorem for the GCHP to approximate it with a diffusion process. Then we construct and solve Hamilton–Jacobi–Bellman (HJB) equation for the expected utility function. The novelty of the results consists of the new Hawkes-based models and in the new optimal investment results in finance and insurance for those models.

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Boumezoued, Alexandre. "Population viewpoint on Hawkes processes." Advances in Applied Probability 48, no. 2 (June 2016): 463–80. http://dx.doi.org/10.1017/apr.2016.10.

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AbstractIn this paper we focus on a class of linear Hawkes processes with general immigrants. These are counting processes with shot-noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of the age pyramid which evolves according to immigration and births. The virtue of this approach that combines an intensity process definition and a branching representation is that the population age pyramid keeps track of all past events. This is used to compute new distribution properties for a class of Hawkes processes with general immigrants which generalize the popular exponential fertility function. The pathwise construction of the Hawkes process and its underlying population is also given.

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Zhang, Chi, Jun He, and Guanghui Yuan. "An Empirical Analysis on DPRK: Will Grain Yield Influence Foreign Policy Tendency?" Sustainability 12, no. 7 (March 30, 2020): 2711. http://dx.doi.org/10.3390/su12072711.

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Democratic People’s Republic of Korea is the hub of Northeast Asia and its geopolitics is of great significance, whose foreign policy trend is not only related to the peace and stability of the region, but also one of the major variables affecting cooperation in Northeast Asia. According to the data on North Korea’s grain yield collected by the Korea National Statistical Office, supplemented by the data on international food aid to North Korea collected by the World Food Programme, and combined with the judgment of 10 experts from China, South Korea and the United States on the Hawk and Dove Index of North Korea’s foreign policy from 1990 to 2018, we use empirical mode decomposition wavelet transform data analysis and feature extraction methods to study the impact relationship, and OLS regression analysis to study the actual cycle of transformation. We found that: (1) North Korea’s grain output is an important indicator that affects its foreign policy tendency (hawks or doves). The hawk refers to those who take a tough attitude in policy and prefer rigid means such as containment, intimidation and conflicts; the dove refers to those who take mild attitude in policy, and prefer to adopt flexible means such as negotiation, cooperation, and coordination. When it comes to grain yield increase, North Korea’s foreign policy tends to be hawkish; when it comes to grain reduction, its dovish tendency will be on the rise. This is because food increase can alleviate grain shortage in North Korea and enhance its ability to adopt tough policies in its foreign policy. However, decreases in grain production will lead to adopt a more moderate policy and seek international cooperation and assistance to ease the internal pressure caused by grain shortage. (2) North Korea’s grain yield influencing its foreign policy (hawks or doves) has a lag phase of about 3 years. Such being the case, the accumulated grain during the production increase period has enhanced North Korea’s ability to cope with grain reduction in the short term. Secondly, the North Korean government blames the reduction on foreign sanctions, which will instead make the North Korean people more determined to resist external pressure. Therefore, we can use the changes in North Korea’s grain output to predict the direction of its foreign policy so as to more accurately judge the development of the Korean Peninsula and more effectively promote the process of peace and cooperation in Northeast Asia. We concluded that grain production will affect its policy sustainability in North Korea.

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Ogura, Hiroshi, Yasutaka Hanada, Hiromi Amano, and Masato Kondo. "Modeling Long-Range Dynamic Correlations of Words in Written Texts with Hawkes Processes." Entropy 24, no. 7 (June 22, 2022): 858. http://dx.doi.org/10.3390/e24070858.

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It has been clarified that words in written texts are classified into two groups called Type-I and Type-II words. The Type-I words are words that exhibit long-range dynamic correlations in written texts while the Type-II words do not show any type of dynamic correlations. Although the stochastic process of yielding Type-II words has been clarified to be a superposition of Poisson point processes with various intensities, there is no definitive model for Type-I words. In this study, we introduce a Hawkes process, which is known as a kind of self-exciting point process, as a candidate for the stochastic process that governs yielding Type-I words; i.e., the purpose of this study is to establish that the Hawkes process is useful to model occurrence patterns of Type-I words in real written texts. The relation between the Hawkes process and an existing model for Type-I words, in which hierarchical structures of written texts are considered to play a central role in yielding dynamic correlations, will also be discussed.

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Guo, Qi, Bruno Remillard, and Anatoliy Swishchuk. "Multivariate General Compound Point Processes in Limit Order Books." Risks 8, no. 3 (September 11, 2020): 98. http://dx.doi.org/10.3390/risks8030098.

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In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. The law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data.

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